(AP) TUCSON, Ariz. - Arizona's police chiefs and county sheriffs hoped a U.S. Supreme Court ruling would settle their long-running debate on what role, if any, they should play in immigration enforcement. Instead, the justices' decision to uphold the state's "show me your papers" statute has left them with more questions than answers.

How long must officers wait for federal authorities to respond when they encounter someone illegal, especially given President Barack Obama's new policy to only deport dangerous criminals and repeat offenders? If they release a person too soon, are they exposing themselves to a lawsuit from residents who accuse them of failing to enforce the law?

How do they avoid being sued for racial profiling? Maricopa County Sheriff Joe Arpaio said he anticipated no change in how he does his job, but that comes from someone who was accused of racially profiling Latinos in a lawsuit filed by the U.S. Justice Department.

"We're going to get sued if we do. We're going to get sued if we don't. That's a terrible position to put law enforcement officers in," said Pima County Sheriff Clarence Dupnik, whose territory covers much of southern Arizona and who has long argued against his state's requirement that local law enforcement be forced to ask about the legal status of anyone suspected of being in the U.S. illegally.

The justices on Monday unanimously approved the Arizona law's most-discussed provision requiring police to check the immigration status of those they stop for other reasons. But it struck down provisions allowing local police to arrest people for federal immigration violations. They also warned against detaining people for any prolonged period merely for not having proper immigration papers.

The decision left police chiefs and sheriffs grappling with questions ranging from what justifies reasonable suspicion that someone is in the country illegally to how long officers must wait when federal authorities are slow to respond to a question on someone's immigration status.

"It's uncharted territory," said Tony Estrada, sheriff of Santa Cruz County on the state's southern border with Mexico. "It's going to be challenging. It's a complicated issue, and it's not going to be solved by this particular decision."

Tucson Police Chief Roberto Villasenor estimates the statute will result in 50,000 additional calls a year to federal immigration authorities in his city alone. That includes 36,000 arrests a year for suspects who are not booked into jail, typically for offenses like disorderly conduct, misdemeanor assault, shoplifting, vandalism and driving more than 25 mph over the speed limit.

Those suspects, who would normally be released with a citation, must be booked into custody if immigration authorities "don't answer the phone, they never call us back after we talk to them or whatever," Villasenor said.

An estimated 14,000 inquiries a year will be for people encountered on street patrol who are not arrested, Villasenor said. They may raise suspicion for their manner of dress, language or other characteristics outlined in guidelines issues to law enforcement agencies statewide.

"I'm not sure (the federal government is) set up to accommodate that workload right now. I hope I'm wrong," said Villasenor, who joined Dupnik and other law enforcement in voicing opposition to the 2010 law in a filing to the Supreme Court.

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The U.S. Department of Homeland Security acknowledged concern about a flood of inquiries but signaled it would only deport people who meet its enforcement priorities. Those priorities are repeat immigration violators, people who pose a public safety or national security threat and recent border crossers.

"The Supreme Court's decision raises the possibility of a significant increase in the number of inquiries, referrals and status verification inquiries from Arizona state authorities that will impact DHS's immigration enforcement operations," the department said Monday in a note to field offices.

Arpaio, the controversial Phoenix lawman known for his anti-immigration raids, said he was concerned whether federal agents will decline to pick up some illegal immigrants who are stopped by his deputies.

"I have my suspicions," he said.

Arpaio asked a federal judge earlier this month to dismiss a lawsuit that claims his office discriminated against Latinos in the sheriff's trademark immigration patrols and had a culture of disregard for basic constitutional rights.

Hours after Monday's ruling, the Department of Homeland Security canceled agreements with seven Arizona police departments that deputized officers to arrest people on immigration violations while on street patrol.

Phoenix Police Chief Daniel Garcia declined to detail how the statute will play out but anticipates it won't be much of a departure from what officers already do.

"It's much too early to try to speculate on these issues of law," he said.

If federal agents decline to pick up immigrants, the state doesn't have any way to force federal authorities to pick them up and will likely have to let them go unless they're suspected of committing a crime that would require them to be brought to jail, said Peter Spiro, a Temple University law professor who specializes in immigration law.

In that sense, the law is symbolic, Spiro said. The questioning requirement "is useful to the extent that it allows states to give notice of hostilities to undocumented immigrants," Spiro said. "It allows for a formal expression of the state's hostilities toward undocumented immigrants."

Arizona Gov. Jan Brewer called the decision a victory for all Americans, but said she expected lawsuits to challenge the implementation of the law.

"It's certainly not the end of our journey," she said.

Responding to criticism that the law would lead to racial profiling, Brewer said that any officer who violates a person's civil rights will be held accountable. Even while upholding the provision, the justices said the status check could be challenged.

Homeland Security Secretary Janet Napolitano said in a written statement that the Supreme Court's ruling will make her agency's work more challenging, but she was pleased that the court ruled state laws can't dictate the federal government's immigration enforcement priorities.

Immigration rights groups said they were surprised and disappointed by the court's decision, and planned to ask the lower courts to block the law.

"The opinion invites the challenges that we are bringing. It's going to cause racial profiling. It will cause prolonged detentions," said Linton Joaquin of the National Immigration Law Center, one of the groups pushing a separate challenge to the law.

Arizona passed the law in 2010, with lawmakers arguing that that federal government wasn't adequately preventing illegal immigration. The Obama administration sued to block it, saying that enforcing immigration laws was a federal responsibility.

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